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PERMISSIONS AND ACKNOWLEDGMENTS

GRATEFUL acknowledgement is hereby made to the following individuals, publishers, and companies for permission to use material that they have provided or to quote from sources for which they hold the rights. Every effort has been made to locate the copyright owners of material reproduced in this book. Omissions that are brought to our attention will be corrected in subsequent editions.

Thanks to William Frucht for the cover photograph of video feedback and for all the photographs in the color insert in Chapter 4.

Thanks to Daniel Hofstadter and Monica Hofstadter for photographs of various loopy structures, used as interludes between chapters.

Thanks to Kellie and Richard Gutman for two photographs in Chapter 4.

Thanks to Jeannel King for her poem “Ode to a Box of Envelopes” in Chapter 7.

Thanks to Silvia Sabatini for the photograph of the lap loop in Anterselva di Mezzo, facing Chapter 8.

Thanks to Peter Rimbey for the photograph of Carol and Douglas Hofstadter facing Chapter 16.

Thanks to David Oleson for his parquet deformation “I at the Center” in Chapter 17.

“Three Kangaroos” logo, designed by David Lance Goines © Ravenswood Winery. Reprinted with permission by Joel Peterson, Ravenswood Winery.

“Three Ravens” logo, designed by David Lance Goines © Ravenswood Winery. Reprinted with permission by Joel Peterson, Ravenswood Winery.

“Peanuts” cartoon, dated 08/14/1960: © United Feature Syndicate, Inc. Reprinted with permission by United Media.

M. C. Escher, Drawing Hands © 2006 M. C. Escher Company, Holland. All rights reserved. www.mcescher.com. Reprinted with permission.

Whitehead, Alfred North and Bertrand Russell, Principia Mathematica (second edition), Volume I (1927), page 629, reprinted in 1973 © Cambridge University Press.

“Nancy” cartoon: “Sluggo dreaming”: © United Feature Syndicate, Inc. Reprinted with permission by United Media.

Morton Salt “Umbrella Girl” © Morton International, Inc. Reprinted with permission of Morton International, Inc.

Excerpt from Karen Horney, Our Inner Conflicts, © 1945 by W. W. Norton &